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School

University of Toronto Mississauga

Department

Sociology

Course

SOC222H5

Professor

John Kervin

Semester

Fall

Description

SOC 222 -- MEASURING the SOCIAL WORLD
Session #12 -- NESTED REGRESSION
CONTEXT of TODAY’S SESSION
• “Statistics and Data Analysis”
What is Data Analysis?
Statistics is about two questions:
1. Is there a relationship
2. Does that relationship also exist in the population
• Art of finding true relationships and true causes (something you can do with)
o Looking at causal processes, ruling out alternative explanations
1. causal processes
2. alternative explanations
• controlling statistically
Today’s Objectives: Know…
1. How statistical control is achieved
2. The difference between experimental and statistical control
3. How to build successive regression models
4. The different kinds of effects when a third variable is added
Terms to Know
causal process alternative explanation
statistical control
causal diagram
Venn diagram
independent effects
spurious effects
indirect effects
interaction effects
experimental control
statistical control
unique effect
CAUSAL PROCESSES
add a second independent variable, T
• Like X, it (T) is a potential cause
• Check covariance, and then check for effect size and significance
Causal Diagrams and Venn Diagrams
Causal Diagrams
• Use arrows to show the causal connections among variables
• Simplest causal diagram is X Y
• Time is part of it, and it goes from left to right
• Time is one of the three requirements, so say something causes
something else (has to come before)
• The causal diagram is a short way to say two things:
1. Variation in x is associated with variation in y (vary together in some systematic way)
2. X comes before y
Venn Diagrams
Each circle represents the variation in a variable
Venn diagram do not indicate causal ordering • Indicate co-variation by overlapping or not overlapping (don’t show systematic
change)
No covariation (no relationship):
X Y
Covariation (a relationship):
X Y
Covariation (a strong relationship)
X Y
ADDING a SECOND IV: “T”
• Hardly throw in another dependent variable, restrict it to 1 dependent variable
1. Independent effects
X
Y
T X Y T
• X and T both covary with (affect) Y
• Each has a direct effect on Y
• They are independent of one another
• Regression check:
• The bivariate results for X don’t change when T is added to the regression
as a second IV
2. Spurious effect
T
Y
X
T
X Y
• T affects (covaries with) both X and Y
• Thus both X and Y will vary together, as a result of changes in T
• As T increases, both X and Y increase
• This makes it seem that X and y are directly related when they aren’t
• Thus the X-Y relationship is spurious (third variable that is causing
both X & Y )
• Regression check: controlling for T, removes X-Y relationship
• T precedes X in time
• When T is added to the regression, the bivariate results for X-Y
disappear
• Controlling for T removes the X-Y relationship 3. Indirect effect; seems X-Y directly related, when they are not (indirectly causes Y)
X
Y
T
T
X Y
• X affects T
• T, in turn, affects Y
• Thus Y will vary when X varies
• This makes it seem that X and Y are directly related when they
aren’t
• Thus the X-Y relationship is indirect
• X does cause Y, but indirectly, through T
• Regression check:
• X precedes T in time
• When T is added to the regression, the bivariate results for X-Y
disappear (because we are controlling the T in the middle)
• Note:
• This is similar to the spurious effect
• Only difference:
• Spurious effect: T comes before X
• Indirect effect: T comes after X 4. Interaction effect: T affects the relationship between X & Y (X-Y depends on T)
X Y
T
T 1
X Y
T 2
X Y
• The X-Y relationship changes
• Depending on the value of T (usually category variable)
• T is usually a category variable (e.g., sex, religion)
• Regression check: separate regression for each category for T (ex, each
religious group) and then see the X-Y relationship
• Run separate regressions for each category of T
• The bivariate X-Y relationship varies as T changes
• Note:
• T does not have to covary with either X or Y
• All it has to do is just changes the X-Y relationship Practice Suggestion
• Practice with the Student data set
REGRESSION and CONTROLLING
(don’t all